Computer Simulations in Many-particle Physics 2

Relations:

During a review of study plans, the course 12PEMC2 can be substituted for the course 12SFMC2.

Course guarantor:

Richard Liska

Lecturer:

Karel Houfek, Milan Předota

Tutor:

Karel Houfek, Milan Předota

Supervisor:

Department of Laser Physics and Photonics

Synopsis:

Advanced methods of Monte Carlo and molecular dynamics and their applications to various problems: critical phenomena, complex molecules, non-equilibrium phenomena, transport coefficients, kinetic MC, optimalization problems, quantum MC, ab initio simulations, Car-Parrinello method.

Requirements:

Syllabus of lectures:

1. Phase transitions and critical phenomena: Methods of inserting particles, Gibbs ensemble, phase equilibrium, critical temperature by scaling with a system size, critical slowing down, cluster algorithms for spin models.

2. Special algorithms and techniques: Random number generation, multispin coding for Ising model and cellular automata.

3. Simulation of realistic systems: Long-range forces, Ewald sumation, simulation of molecular systems, metods conserving bond length and angles.

4. Non-equilibrium systems close to equilibrium: Calculation of kinetic coefficients, time correlation functions, Einstein relation, non-equilibrium MD, self-diffusion in lattice gas, equilibrium and con-equilibrium calculation of viscosity and dielectrical constant, model of adsorption and desorption, kinetic MC - from growth of real materials to econophysics, choice of kinetics, time in kinetic MC, „n-fold way“ algorithm.

5. Simulation of growth processes: SOS models, simulation of simple growth models (Eden, Edwars-Wilkinson model etc.), , kinetic roughening, Laplacian growth, diffusion limited aggregation (DLA), realistic simulations of crystal growth.

6. Optimalization problems: Traveling salesman problem, simulated annealing, calculation of diffusion in lattice gas, calculation of energy barriers by molecular statics, finding the minimal energy path in a system on N particles, method „elastic nudged band“.

7. Quantum simulations: System of interacting electrons and ions, from N-atom continuous system to simple lattice quantum models (Hubbarduv model), variational quantum MC, canonical quantum MC, isomorphism of quantum and classical systems, sign problem, firt principle calculations, method of density functional, Car-Parrinello metods.

Syllabus of tutorials:

Study Objective:

Knowledge:

Advanced knowledge of physics of many particles.

Skills:

Ability to use advanced particle simulations.

Study materials:

Key references:

[1] I. Nezbeda, J. Kolafa, M. Kotrla, Úvod do počítačových simulací: Metody Monte Carlo a molekuární dynamiky, Karolinum, 2003.

Recommended references:

[2] D. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge University Press, 2002.

[3] M.E.J. Newman, G.T. Barkema, Monte Carlo Methods in Statistical Physics, Oxford University Press, 2002.

[4] D. Frenkel, B. Smit, Understanding molecular simulation, Academic Press, San Diego, USA, 2002.

[5] A. L. Barabasi, H. E. Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, 1995.

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzika plazmatu a termojaderné fúze (elective course)
• Fyzikální elektronika - Počítačová fyzika (elective course)